1. Combinational Logic Circuits

2. Comb. Logic in Context Typically part of system with storage
Computer looks like this at high level

3. Decoders
n to 2n decoder
n inputs
2n outputs
For each input, one and only one output will be active.

4. 2 to 4 Decoder – Truth TableX1 X0 Y3 Y2 Y1 Y0 1

5. 2 to 4 Decoder Equations

6. 2-to-4 Line Decoder

7. 2-to-4 with Enable

8. Truth Table, 3-to-8 Decoder
Notice they are minterms

9. Schematic

10. Uses for Decoders Binary number might serve to select some operation
Computer op codes are encoded
Decoder lines might select add, or subtract, or multiply, etc.
Memory address lines

11. Encoder Encoder is the opposite of decoder
2n inputs (or less – maybe BCD in)
n outputs

12. Truth Table

13. Inputs are Minterms Can OR them together appropriately
A0 = D1 + D3 + D5 + D7

14. What’s the Problem? What if D3 and D6 both high?
Simple OR circuit will set A to 7

15. Priority Encoder Chooses one with highest priority Note “don’t cares”
Largest number, usually
Note “don’t cares”
What if all inputs are zero?

16. Need Another Output
A “Valid” output

17. Valid is OR of inputs

18. Multiplexer(MUX)/Data Selector
N to 1 multiplexer
n data input lines
Log2(n) control inputs
One output
This circuit will “connect” the selected input to the output. The selected input is specified by a decoding of the control inputs.

19. Multiplexer (or Mux)
Selects one of a set of inputs to pass on to output
Binary control code, n lines
Choose from 2n inputs
Useful for choosing from sets of data
Memory or register to ALU
Very common
74153

20. Two Input Mux

21. Logic

22. Logic is Decoder Plus

23. Three-State Implementation

24. Demultiplexer Takes one input Out to one of 2n possible outputs

25. Demux is a Decoder
With an enable

26. Code Converters One code to another
Book puts seven-segment decoder in this category
Typically multiple outputs
Each output has function or truth table

27. Seven-Segment Decoder
This Friday’s lab: Verilog of hex to LEDs
Extended version of book example
You may want to work out mapping (truth table/function) before lab